What frequency and waveguide/horn size do you consider as a limit for home reproduction?

Does it matter that there is little directivity control at the lower frequencies? Bass is generally assumed to be omnidirectional and if low enough in frequency then also non stereo.

If we want a horn/waveguide to perform down to, say 100Hz, what sort of impractical constraints need to be achieved to get this?

The listening room in my house is bigger than the apartment I lived in a few years ago, and it's *still* too small for these speakers. Believe me, there's a point of diminishing returns when it comes to waveguides. Nobody needs a loudspeaker that's so large that you have to buy a new house to listen to them.

You may want to look at the Pi 7 corner horn. I don't know all the details, but I think by using a 24 inch horn, and the walls of the room, it has controlled directivity down to maybe ~300 or 400 Hz.

Calling a speaker in a corner a 90 degree waveguide is somewhat shaky IMO. I only consider the concept of "directivity" as being free field. To me, it is not applicable to the situation that you describe, because then anything placed in a corner is 90 degree CD. But there is a price to pay for this and they are called HOM. The HOM content from a corner loaded situation would be extremely high, making this not only less than desirable, but, again IMO, something to be completely avoided.

Earl, can the HOMs be seen using a velocity microphone (or microflown) inserted into a waveguide to sense side-to-side wave energy? I'm wondering what this would look like, with something like MLS or chirp drive. Or would putting the microphone into that area cause too much disruption itself?

Not only would it work, but its been done. Makarski at Achen, did this with a horn. He measured very distinct not uniform motion in the wavefront. However, because this motion did not have a strong influence on the polar patern he concluded that it was not important. But wait! Says I. Not having a significant influence on the polar response and not be audible are distinctly different things. I think this is why the paper was only ever a preprint and not a full paper. He knew that he could not draw any audibility conclusions from what he found, but he clearly showed HOMs in action. It was only a few years later that Lidia and I published (although we already had the data) how small time perturbations - like HOM - could be audible well below the point of actually having a notable effect on the polar pattern. And most significantly - that these effects become MORE audible at higher SPLs. Can you say "horn harshness"? - very subtle time delayed echos, that can be quite annoying.

To me, the case is pretty much closed. Although the ney-sayers still persist to this day with their wild unsubstantiated beliefs.

Ok, Earl, thanks. I might give it a try. I ran across a biological paper where some people researching insect sounds made a velocity microphone by essentially cutting the back off a cheap electret condenser mic capsule, and had good results. That doesn't seem like it should be overly difficult (though it might take destroying a small handful of capsules before one survives the trauma).

The better ones use a hot wire and measure resistance changes. Almost no effect on the velocity field. Your approach might be very insensitive for a sensor small enough to not destroy the field you are trying to measure. Depends on the frequency range you want of course. Makarski went up to 10 k I believe. That takes a pretty small sensor.

Calling a speaker in a corner a 90 degree waveguide is somewhat shaky IMO. I only consider the concept of "directivity" as being free field. To me, it is not applicable to the situation that you describe, because then anything placed in a corner is 90 degree CD. But there is a price to pay for this and they are called HOM. The HOM content from a corner loaded situation would be extremely high, making this not only less than desirable, but, again IMO, something to be completely avoided.

I some recall that in one of your papers you mentioned that absorptive surface wave guide might help reduce reduce HOMs. If we had sufficient frequency dependant absorption, wouldn't it be beneficial for usng such corner?

Lets say that the walls were somehow made entirely absorptive. Then the situation is indistinguishable from a free field, and there is no "waveguide" effect. So the whole discussion is moot. Reality will lie somewhere between reflective walls, a waveguide effect and HOMs, or absorptive walls, no waveguide effect and no HOMs. What is not possible is a waveguide effect and no HOM.

I disagree. There will still be directionality applied relative to free field. It won't be the same as a waveguide, most specifically it won't have the axial response track power response, but "Waveguide effect" must incorporate directionality in its definition or it's meaningless. After all, the elimination of boundary effects is a big part of why people use horns and waveguides in the first place.

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